Contents Chapter 1. Introduction 1 Chapter 2. Basic notions of representation theory 5 §2.1. What is representation theory? 5 §2.2. Algebras 8 §2.3. Representations 9 §2.4. Ideals 15 §2.5. Quotients 15 §2.6. Algebras defined by generators and relations 16 §2.7. Examples of algebras 17 §2.8. Quivers 19 §2.9. Lie algebras 22 §2.10. Historical interlude: Sophus Lie’s trials and transformations 26 §2.11. Tensor products 30 §2.12. The tensor algebra 35 §2.13. Hilbert’s third problem 36 §2.14. Tensor products and duals of representations of Lie algebras 36 §2.15. Representations of sl(2) 37 iii
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